Question : The volume of a solid hemisphere is 19404 cm3. Its total surface area is:
Option 1: 4158 cm2
Option 2: 2858 cm2
Option 3: 1738 cm2
Option 4: 2038 cm2
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Correct Answer: 4158 cm 2
Solution :
Given: Volume of solid hemisphere = 19404 cm
3
Let the radius of the hemisphere be $r$.
We know, volume of a hemisphere $= \frac{2}{3}\pi r^3$
$⇒ 19404 = \frac{2}{3}\pi r^3$
$⇒ 19404 = \frac{2}{3}\times\frac{22}{7}\times r^3$
$\therefore r= 21$
Total surface area of the hemisphere $= 3\pi r^2 = 3\times\frac{22}{7}\times21\times21= 4158$ cm
2
Hence, the correct answer is 4158 cm
2
.
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